Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. The Howard methods also assume that the species composition of the harvests are equal to the species composition of released fish, which may not be true and is evident in the logbook data. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds that when not met, values are borrowed from nearby areas Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is no uncertainty generated from uncertainty in the assmptions made such as species composition of the releases or when borrowing values from one area to another. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.
Time series 1999 - present 1977 - present

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was explored that loosened the assumption that logbook releases were a census. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Priors.

Priors range from uninformative to very informative or fixed. These will be covered once a satisfactorilly convergerd model is achieved.

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behavior and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 8.**- DSR rockfish (including yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 10.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 12.**- Residuals from logbook harvests

Figure 12.- Residuals from logbook harvests


SWHS residuals

**Figure 13.**- Residuals from SWHS harvests.

Figure 13.- Residuals from SWHS harvests.



**Figure 14.**- Residual of SWHS releases

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 15.**- Mean percent of harvest by charter anglers.

Figure 15.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 16.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 18.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 19.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 20.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


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SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 23.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 24.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 25.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 26.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 27.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 28.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 30.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 31.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_black 2 4.689112
beta0_black 2 2.787117
beta3_black 2 1.901605
beta2_black 1 1.571803
beta3_pH 2 1.434811
tau_beta0_pH 1 1.412482
beta1_pH 2 1.363478
beta0_pH 2 1.360402
beta1_yellow 4 1.354796
parameter n badRhat_avg
beta1_pelagic 1 1.315278
sd_comp 1 1.246095
beta0_pelagic 1 1.240208
beta2_pH 5 1.229701
beta2_pelagic 2 1.208656
tau_beta0_pelagic 1 1.158077
beta4_pelagic 2 1.142460
tau_beta0_black 1 1.117010
Table 2. Summary of unconverged parameters by area
afognak BSAI CI eastside NG northeast NSEI PWSI PWSO SOKO2SAP WKMA
beta0_black 0 0 1 0 0 0 1 0 0 0 0
beta0_pelagic 0 0 0 0 0 0 0 1 0 0 0
beta0_pH 0 0 1 0 0 0 0 0 1 0 0
beta1_black 0 0 1 0 0 0 1 0 0 0 0
beta1_pelagic 0 0 0 0 0 0 0 1 0 0 0
beta1_pH 0 0 1 0 0 0 0 1 0 0 0
beta1_yellow 1 0 0 1 0 1 0 0 1 0 0
beta2_black 0 0 0 0 0 0 1 0 0 0 0
beta2_pelagic 0 0 0 0 0 0 0 1 1 0 0
beta2_pH 0 0 1 0 1 0 0 1 1 0 1
beta3_black 0 0 1 0 0 0 1 0 0 0 0
beta3_pH 0 0 1 0 0 0 0 0 1 0 0
beta4_pelagic 0 1 0 0 0 0 0 0 0 1 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_black 0 0 0 0 0 0 0 1 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 1 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.124 0.074 -0.260 -0.128 0.028
mu_bc_H[2] -0.094 0.046 -0.172 -0.098 0.011
mu_bc_H[3] -0.432 0.072 -0.566 -0.435 -0.284
mu_bc_H[4] -0.985 0.198 -1.381 -0.987 -0.594
mu_bc_H[5] 0.920 0.908 -0.130 0.742 3.221
mu_bc_H[6] -2.168 0.317 -2.795 -2.162 -1.571
mu_bc_H[7] -0.446 0.109 -0.664 -0.445 -0.235
mu_bc_H[8] 0.247 0.372 -0.347 0.217 1.035
mu_bc_H[9] -0.295 0.136 -0.559 -0.293 -0.032
mu_bc_H[10] -0.108 0.069 -0.235 -0.110 0.034
mu_bc_H[11] -0.122 0.038 -0.196 -0.122 -0.047
mu_bc_H[12] -0.254 0.106 -0.476 -0.248 -0.054
mu_bc_H[13] -0.132 0.078 -0.285 -0.132 0.022
mu_bc_H[14] -0.301 0.095 -0.491 -0.299 -0.117
mu_bc_H[15] -0.341 0.050 -0.437 -0.343 -0.241
mu_bc_H[16] -0.264 0.384 -0.921 -0.291 0.579
mu_bc_R[1] 1.352 0.145 1.072 1.348 1.633
mu_bc_R[2] 1.453 0.089 1.275 1.454 1.624
mu_bc_R[3] 1.399 0.142 1.112 1.401 1.676
mu_bc_R[4] 0.907 0.203 0.496 0.912 1.285
mu_bc_R[5] 1.161 0.458 0.241 1.175 2.083
mu_bc_R[6] -1.588 0.422 -2.424 -1.584 -0.749
mu_bc_R[7] 0.397 0.187 0.020 0.399 0.747
mu_bc_R[8] 0.550 0.195 0.158 0.557 0.915
mu_bc_R[9] 0.335 0.202 -0.109 0.355 0.688
mu_bc_R[10] 1.296 0.137 1.012 1.301 1.565
mu_bc_R[11] 1.034 0.097 0.846 1.035 1.227
mu_bc_R[12] 0.820 0.208 0.417 0.818 1.227
mu_bc_R[13] 1.030 0.102 0.817 1.031 1.229
mu_bc_R[14] 0.897 0.143 0.610 0.901 1.175
mu_bc_R[15] 0.782 0.110 0.565 0.783 0.997
mu_bc_R[16] 1.095 0.124 0.841 1.097 1.330
tau_pH[1] 5.106 0.578 3.558 5.145 6.106
tau_pH[2] 2.057 0.226 1.657 2.044 2.527
tau_pH[3] 2.179 0.252 1.711 2.178 2.674
beta0_pH[1,1] 0.559 0.179 0.198 0.557 0.897
beta0_pH[2,1] 1.373 0.183 1.006 1.377 1.718
beta0_pH[3,1] 1.436 0.202 1.012 1.451 1.782
beta0_pH[4,1] 1.664 0.375 1.119 1.617 2.878
beta0_pH[5,1] -0.850 0.284 -1.460 -0.829 -0.357
beta0_pH[6,1] -0.660 0.452 -1.776 -0.590 -0.023
beta0_pH[7,1] -0.443 0.458 -1.403 -0.420 0.483
beta0_pH[8,1] -0.656 0.289 -1.293 -0.629 -0.186
beta0_pH[9,1] -0.646 0.283 -1.271 -0.632 -0.144
beta0_pH[10,1] 0.242 0.208 -0.191 0.247 0.628
beta0_pH[11,1] -0.093 0.177 -0.469 -0.084 0.231
beta0_pH[12,1] 0.476 0.190 0.097 0.476 0.841
beta0_pH[13,1] -0.002 0.145 -0.302 0.001 0.280
beta0_pH[14,1] -0.311 0.168 -0.653 -0.307 0.014
beta0_pH[15,1] -0.037 0.186 -0.418 -0.035 0.336
beta0_pH[16,1] -0.440 0.335 -1.214 -0.386 0.082
beta0_pH[1,2] 2.814 0.163 2.476 2.820 3.121
beta0_pH[2,2] 2.880 0.136 2.610 2.879 3.137
beta0_pH[3,2] 3.112 0.182 2.782 3.119 3.422
beta0_pH[4,2] 2.943 0.134 2.689 2.944 3.202
beta0_pH[5,2] 4.744 1.326 3.046 4.487 8.111
beta0_pH[6,2] 3.113 0.201 2.720 3.116 3.510
beta0_pH[7,2] 1.955 0.171 1.624 1.957 2.290
beta0_pH[8,2] 2.876 0.170 2.532 2.877 3.215
beta0_pH[9,2] 3.435 0.214 3.021 3.432 3.859
beta0_pH[10,2] 3.741 0.194 3.366 3.740 4.115
beta0_pH[11,2] -4.846 0.310 -5.480 -4.847 -4.255
beta0_pH[12,2] -4.787 0.403 -5.602 -4.779 -3.987
beta0_pH[13,2] -4.586 0.387 -5.336 -4.595 -3.787
beta0_pH[14,2] -5.613 0.465 -6.568 -5.601 -4.768
beta0_pH[15,2] -4.294 0.350 -4.975 -4.295 -3.588
beta0_pH[16,2] -4.882 0.379 -5.631 -4.883 -4.152
beta0_pH[1,3] 0.602 1.078 -1.683 0.571 2.134
beta0_pH[2,3] 2.201 0.159 1.894 2.202 2.509
beta0_pH[3,3] 2.526 0.147 2.250 2.524 2.818
beta0_pH[4,3] 2.960 0.163 2.634 2.965 3.283
beta0_pH[5,3] 1.401 1.679 -1.070 1.076 5.555
beta0_pH[6,3] -0.839 0.835 -2.223 -0.947 1.334
beta0_pH[7,3] -1.801 0.425 -2.646 -1.794 -0.995
beta0_pH[8,3] 0.280 0.188 -0.082 0.284 0.639
beta0_pH[9,3] -0.866 0.557 -2.444 -0.740 -0.173
beta0_pH[10,3] 0.395 0.414 -0.629 0.475 1.015
beta0_pH[11,3] -0.138 0.326 -0.770 -0.134 0.502
beta0_pH[12,3] -0.860 0.358 -1.621 -0.833 -0.227
beta0_pH[13,3] -0.115 0.308 -0.703 -0.119 0.490
beta0_pH[14,3] -0.270 0.264 -0.791 -0.264 0.247
beta0_pH[15,3] -0.718 0.304 -1.324 -0.705 -0.154
beta0_pH[16,3] -0.375 0.284 -0.933 -0.377 0.177
beta1_pH[1,1] 3.050 0.330 2.457 3.035 3.736
beta1_pH[2,1] 2.150 0.299 1.629 2.126 2.804
beta1_pH[3,1] 1.962 0.331 1.412 1.932 2.697
beta1_pH[4,1] 2.357 0.461 1.561 2.326 3.322
beta1_pH[5,1] 2.287 0.355 1.702 2.254 3.119
beta1_pH[6,1] 3.802 1.101 2.338 3.568 6.565
beta1_pH[7,1] 2.575 0.902 0.816 2.526 4.484
beta1_pH[8,1] 4.034 1.051 2.601 3.797 6.627
beta1_pH[9,1] 2.328 0.382 1.685 2.297 3.196
beta1_pH[10,1] 2.387 0.289 1.852 2.373 2.994
beta1_pH[11,1] 3.271 0.222 2.853 3.258 3.737
beta1_pH[12,1] 2.560 0.223 2.144 2.551 2.997
beta1_pH[13,1] 2.970 0.214 2.583 2.964 3.418
beta1_pH[14,1] 3.409 0.221 2.993 3.402 3.867
beta1_pH[15,1] 2.543 0.229 2.097 2.542 2.992
beta1_pH[16,1] 4.069 0.621 3.169 3.948 5.551
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.028 0.181 0.000 0.000 0.323
beta1_pH[4,2] 0.004 0.071 0.000 0.000 0.004
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.689 0.340 6.065 6.688 7.374
beta1_pH[12,2] 6.453 0.462 5.599 6.431 7.417
beta1_pH[13,2] 6.969 0.427 6.114 6.970 7.838
beta1_pH[14,2] 7.253 0.485 6.340 7.234 8.246
beta1_pH[15,2] 6.772 0.382 6.030 6.766 7.525
beta1_pH[16,2] 7.475 0.415 6.683 7.474 8.305
beta1_pH[1,3] 2.995 2.356 0.000 2.972 7.744
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.179 1.546 1.633 2.914 6.322
beta1_pH[6,3] 2.617 0.682 1.384 2.591 3.957
beta1_pH[7,3] 2.665 0.428 1.815 2.660 3.496
beta1_pH[8,3] 2.780 0.337 2.119 2.772 3.446
beta1_pH[9,3] 2.949 0.559 2.176 2.850 4.458
beta1_pH[10,3] 2.972 0.475 2.223 2.906 4.170
beta1_pH[11,3] 2.717 0.384 1.994 2.707 3.504
beta1_pH[12,3] 4.114 0.448 3.303 4.101 5.012
beta1_pH[13,3] 1.708 0.327 1.078 1.708 2.356
beta1_pH[14,3] 2.510 0.338 1.849 2.507 3.171
beta1_pH[15,3] 2.008 0.323 1.398 2.002 2.659
beta1_pH[16,3] 1.782 0.316 1.172 1.777 2.406
beta2_pH[1,1] 0.489 0.173 0.292 0.467 0.788
beta2_pH[2,1] 0.644 0.579 0.245 0.527 1.787
beta2_pH[3,1] 0.740 0.697 0.219 0.572 2.590
beta2_pH[4,1] 0.249 0.955 -3.506 0.436 0.930
beta2_pH[5,1] 1.403 0.950 0.223 1.271 3.696
beta2_pH[6,1] 0.188 0.066 0.090 0.179 0.342
beta2_pH[7,1] 0.011 0.060 0.000 0.000 0.068
beta2_pH[8,1] 0.246 0.096 0.124 0.229 0.458
beta2_pH[9,1] 0.434 0.217 0.176 0.395 0.922
beta2_pH[10,1] 0.615 0.307 0.285 0.555 1.240
beta2_pH[11,1] 0.788 0.210 0.473 0.759 1.268
beta2_pH[12,1] 1.337 0.494 0.731 1.231 2.577
beta2_pH[13,1] 0.743 0.223 0.415 0.712 1.276
beta2_pH[14,1] 0.835 0.211 0.527 0.803 1.334
beta2_pH[15,1] 0.793 0.278 0.415 0.741 1.496
beta2_pH[16,1] 0.387 0.177 0.172 0.338 0.838
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -0.548 3.984 -8.633 -0.554 7.052
beta2_pH[4,2] -0.561 4.043 -8.495 -0.641 7.777
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.196 4.129 -19.608 -8.318 -3.894
beta2_pH[12,2] -7.754 4.721 -19.064 -7.051 -1.015
beta2_pH[13,2] -7.534 4.724 -19.149 -6.554 -1.651
beta2_pH[14,2] -8.158 4.397 -19.009 -7.115 -2.527
beta2_pH[15,2] -8.988 4.154 -19.543 -8.095 -3.750
beta2_pH[16,2] -9.218 4.092 -19.462 -8.348 -3.974
beta2_pH[1,3] 0.374 1.768 0.000 0.180 1.343
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.775 6.180 0.367 7.544 23.088
beta2_pH[6,3] 8.965 6.133 0.494 7.815 23.113
beta2_pH[7,3] 8.894 6.090 1.068 7.720 23.370
beta2_pH[8,3] 9.767 5.676 1.849 8.690 23.455
beta2_pH[9,3] 8.325 6.556 0.379 7.134 23.977
beta2_pH[10,3] 7.988 6.524 0.453 6.784 22.653
beta2_pH[11,3] -2.327 2.139 -8.413 -1.718 -0.622
beta2_pH[12,3] -2.453 2.034 -8.322 -1.858 -0.935
beta2_pH[13,3] -2.914 2.346 -9.984 -2.170 -0.797
beta2_pH[14,3] -2.904 2.326 -9.412 -2.141 -0.924
beta2_pH[15,3] -3.005 2.292 -9.323 -2.285 -1.003
beta2_pH[16,3] -3.077 2.485 -9.927 -2.270 -0.909
beta3_pH[1,1] 35.904 0.850 34.371 35.864 37.668
beta3_pH[2,1] 33.626 1.202 31.603 33.529 36.399
beta3_pH[3,1] 33.698 1.019 31.784 33.673 35.739
beta3_pH[4,1] 32.976 3.540 19.751 33.685 36.274
beta3_pH[5,1] 27.812 1.244 26.485 27.507 31.298
beta3_pH[6,1] 38.577 3.021 32.932 38.394 44.904
beta3_pH[7,1] 30.721 7.990 18.541 30.399 45.089
beta3_pH[8,1] 40.043 2.204 36.277 39.728 45.030
beta3_pH[9,1] 30.693 1.490 28.055 30.622 33.823
beta3_pH[10,1] 32.742 0.950 30.991 32.705 34.683
beta3_pH[11,1] 30.324 0.476 29.413 30.311 31.253
beta3_pH[12,1] 30.149 0.408 29.329 30.158 30.940
beta3_pH[13,1] 33.144 0.583 32.031 33.126 34.349
beta3_pH[14,1] 32.033 0.458 31.175 32.016 32.962
beta3_pH[15,1] 31.201 0.650 29.902 31.201 32.488
beta3_pH[16,1] 32.109 1.042 30.467 31.982 34.567
beta3_pH[1,2] 29.844 7.893 18.470 28.738 44.887
beta3_pH[2,2] 29.926 7.879 18.473 29.127 44.649
beta3_pH[3,2] 30.325 8.065 18.421 29.292 45.013
beta3_pH[4,2] 30.152 8.119 18.442 29.366 44.815
beta3_pH[5,2] 29.887 7.966 18.438 29.031 44.835
beta3_pH[6,2] 30.080 8.080 18.356 29.137 44.941
beta3_pH[7,2] 30.279 7.921 18.514 29.495 44.936
beta3_pH[8,2] 30.036 7.947 18.430 29.262 44.771
beta3_pH[9,2] 30.050 7.983 18.453 29.424 44.845
beta3_pH[10,2] 29.777 7.983 18.388 28.866 44.817
beta3_pH[11,2] 43.402 0.177 43.122 43.382 43.779
beta3_pH[12,2] 43.189 0.188 42.929 43.145 43.672
beta3_pH[13,2] 43.872 0.138 43.518 43.907 44.044
beta3_pH[14,2] 43.304 0.201 43.056 43.256 43.799
beta3_pH[15,2] 43.410 0.191 43.103 43.392 43.811
beta3_pH[16,2] 43.493 0.186 43.159 43.491 43.837
beta3_pH[1,3] 36.979 6.173 20.082 38.443 45.104
beta3_pH[2,3] 30.043 7.965 18.437 29.182 45.079
beta3_pH[3,3] 30.219 7.956 18.474 29.230 44.974
beta3_pH[4,3] 30.192 7.943 18.545 29.466 44.875
beta3_pH[5,3] 25.707 6.487 18.229 23.837 42.311
beta3_pH[6,3] 27.163 4.884 19.382 25.931 42.827
beta3_pH[7,3] 26.912 0.982 25.384 26.699 29.179
beta3_pH[8,3] 41.482 0.251 41.041 41.476 41.938
beta3_pH[9,3] 33.043 1.388 28.841 33.456 34.188
beta3_pH[10,3] 35.689 0.898 33.220 35.967 36.830
beta3_pH[11,3] 41.780 0.819 40.127 41.838 43.269
beta3_pH[12,3] 41.731 0.390 40.964 41.744 42.503
beta3_pH[13,3] 42.648 0.834 41.020 42.667 44.272
beta3_pH[14,3] 41.106 0.573 39.925 41.119 42.191
beta3_pH[15,3] 42.626 0.658 41.124 42.695 43.727
beta3_pH[16,3] 42.860 0.747 41.166 42.970 44.075
beta0_pelagic[1] 2.207 0.136 1.940 2.207 2.477
beta0_pelagic[2] 1.520 0.130 1.270 1.520 1.780
beta0_pelagic[3] -0.166 0.871 -2.208 -0.017 0.945
beta0_pelagic[4] 0.502 0.577 -0.828 0.662 1.210
beta0_pelagic[5] 1.192 0.258 0.647 1.198 1.664
beta0_pelagic[6] 1.474 0.262 0.931 1.487 1.956
beta0_pelagic[7] 1.693 0.228 1.316 1.670 2.209
beta0_pelagic[8] 1.765 0.205 1.377 1.759 2.194
beta0_pelagic[9] 2.495 0.310 1.881 2.501 3.051
beta0_pelagic[10] 2.534 0.201 2.105 2.538 2.926
beta0_pelagic[11] 0.064 0.447 -0.953 0.108 0.735
beta0_pelagic[12] 1.681 0.150 1.386 1.682 1.964
beta0_pelagic[13] 0.291 0.238 -0.257 0.317 0.663
beta0_pelagic[14] -0.095 0.289 -0.773 -0.070 0.390
beta0_pelagic[15] -0.260 0.149 -0.547 -0.259 0.040
beta0_pelagic[16] 0.365 0.207 -0.150 0.394 0.693
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.613 1.530 0.000 1.373 5.623
beta1_pelagic[4] 0.675 0.722 0.000 0.525 2.183
beta1_pelagic[5] -0.076 0.318 -0.689 -0.079 0.559
beta1_pelagic[6] -0.103 0.441 -0.874 -0.151 0.727
beta1_pelagic[7] -0.007 0.343 -0.649 -0.017 0.669
beta1_pelagic[8] -0.004 0.282 -0.548 -0.003 0.564
beta1_pelagic[9] 0.181 0.479 -0.755 0.283 0.939
beta1_pelagic[10] 0.064 0.263 -0.430 0.066 0.582
beta1_pelagic[11] 3.685 1.115 2.111 3.508 6.141
beta1_pelagic[12] 2.783 0.315 2.204 2.774 3.389
beta1_pelagic[13] 3.002 0.755 1.861 2.883 4.727
beta1_pelagic[14] 4.282 1.068 2.771 4.060 6.710
beta1_pelagic[15] 2.927 0.267 2.390 2.924 3.459
beta1_pelagic[16] 3.331 0.575 2.619 3.226 5.150
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.170 1.059 0.000 0.081 0.668
beta2_pelagic[4] 0.875 3.464 0.000 0.122 6.232
beta2_pelagic[5] -0.009 0.675 -1.426 -0.010 1.477
beta2_pelagic[6] -0.110 0.703 -1.520 -0.151 1.395
beta2_pelagic[7] -0.016 0.671 -1.490 -0.008 1.354
beta2_pelagic[8] -0.044 0.651 -1.455 -0.024 1.304
beta2_pelagic[9] 0.188 0.685 -1.266 0.237 1.551
beta2_pelagic[10] -0.011 0.636 -1.360 0.006 1.253
beta2_pelagic[11] 1.770 3.645 0.114 0.257 12.840
beta2_pelagic[12] 6.404 5.280 1.146 4.797 21.007
beta2_pelagic[13] 0.845 1.758 0.173 0.446 4.027
beta2_pelagic[14] 0.336 0.240 0.155 0.293 0.744
beta2_pelagic[15] 6.485 5.003 1.366 5.134 20.052
beta2_pelagic[16] 5.417 5.429 0.260 3.989 20.340
beta3_pelagic[1] 29.900 7.912 18.446 28.790 44.901
beta3_pelagic[2] 29.669 7.881 18.519 28.534 44.767
beta3_pelagic[3] 30.217 7.198 18.855 29.388 44.621
beta3_pelagic[4] 27.879 6.562 18.835 26.120 43.500
beta3_pelagic[5] 29.935 8.162 18.542 28.538 45.239
beta3_pelagic[6] 31.883 6.949 18.872 32.033 44.288
beta3_pelagic[7] 29.145 7.418 18.437 28.082 44.728
beta3_pelagic[8] 29.460 7.955 18.341 27.988 44.516
beta3_pelagic[9] 30.784 6.213 19.190 30.736 43.353
beta3_pelagic[10] 29.535 8.162 18.380 28.110 45.064
beta3_pelagic[11] 42.444 1.921 37.272 42.993 45.459
beta3_pelagic[12] 43.463 0.288 42.984 43.456 43.967
beta3_pelagic[13] 42.865 1.364 40.223 42.852 45.611
beta3_pelagic[14] 42.288 1.735 38.811 42.243 45.574
beta3_pelagic[15] 43.189 0.258 42.575 43.192 43.678
beta3_pelagic[16] 43.110 0.571 41.562 43.201 43.833
mu_beta0_pelagic[1] 0.963 0.945 -1.088 1.061 2.760
mu_beta0_pelagic[2] 1.826 0.379 1.040 1.842 2.540
mu_beta0_pelagic[3] 0.320 0.472 -0.673 0.336 1.216
tau_beta0_pelagic[1] 0.894 1.224 0.053 0.477 4.395
tau_beta0_pelagic[2] 2.745 2.635 0.276 1.991 9.802
tau_beta0_pelagic[3] 1.546 1.174 0.183 1.244 4.416
beta0_yellow[1] -0.510 0.177 -0.876 -0.499 -0.195
beta0_yellow[2] 0.517 0.157 0.209 0.515 0.818
beta0_yellow[3] -0.281 0.183 -0.640 -0.278 0.071
beta0_yellow[4] 0.863 0.288 0.025 0.907 1.220
beta0_yellow[5] -0.308 0.350 -0.974 -0.303 0.376
beta0_yellow[6] 1.134 0.171 0.792 1.137 1.463
beta0_yellow[7] 1.066 0.162 0.750 1.066 1.383
beta0_yellow[8] 1.011 0.161 0.691 1.014 1.321
beta0_yellow[9] 0.661 0.164 0.337 0.662 0.971
beta0_yellow[10] 0.582 0.145 0.302 0.581 0.856
beta0_yellow[11] -1.955 0.461 -2.859 -1.956 -1.071
beta0_yellow[12] -3.708 0.442 -4.609 -3.682 -2.900
beta0_yellow[13] -3.738 0.514 -4.871 -3.699 -2.803
beta0_yellow[14] -2.122 0.563 -3.104 -2.165 -0.752
beta0_yellow[15] -2.834 0.449 -3.786 -2.791 -2.066
beta0_yellow[16] -2.408 0.474 -3.335 -2.411 -1.443
beta1_yellow[1] 0.623 0.916 0.000 0.449 2.411
beta1_yellow[2] 1.012 0.284 0.559 0.991 1.526
beta1_yellow[3] 0.636 0.266 0.043 0.644 1.122
beta1_yellow[4] 1.275 0.706 0.641 1.120 3.647
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.035 0.084 0.000 0.000 0.293
beta1_yellow[9] 0.028 0.113 0.000 0.000 0.446
beta1_yellow[10] 0.007 0.022 0.000 0.000 0.086
beta1_yellow[11] 2.103 0.462 1.228 2.091 3.055
beta1_yellow[12] 2.500 0.458 1.638 2.478 3.446
beta1_yellow[13] 2.852 0.508 1.934 2.810 3.929
beta1_yellow[14] 2.197 0.548 0.954 2.228 3.206
beta1_yellow[15] 2.078 0.447 1.295 2.040 3.042
beta1_yellow[16] 2.166 0.476 1.228 2.180 3.102
beta2_yellow[1] -4.903 3.471 -12.539 -4.355 -0.115
beta2_yellow[2] -4.846 3.430 -11.758 -4.164 -0.337
beta2_yellow[3] -4.839 3.489 -12.461 -4.275 -0.248
beta2_yellow[4] -4.388 3.566 -11.883 -3.683 -0.100
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] -5.613 3.628 -13.206 -5.314 -0.142
beta2_yellow[9] -5.482 3.564 -12.981 -5.205 -0.011
beta2_yellow[10] -5.464 3.469 -12.972 -5.210 -0.195
beta2_yellow[11] -5.226 2.980 -12.021 -4.707 -1.084
beta2_yellow[12] -5.360 2.749 -11.647 -4.875 -1.430
beta2_yellow[13] -5.368 2.826 -11.928 -4.820 -1.586
beta2_yellow[14] -5.564 3.059 -12.760 -5.079 -0.853
beta2_yellow[15] -5.021 2.910 -11.684 -4.412 -1.127
beta2_yellow[16] -5.608 2.967 -12.423 -5.094 -1.390
beta3_yellow[1] 26.717 7.386 18.372 23.586 44.448
beta3_yellow[2] 29.164 1.535 27.191 28.871 32.819
beta3_yellow[3] 32.758 3.218 23.810 32.812 38.843
beta3_yellow[4] 29.161 3.481 22.378 27.998 36.160
beta3_yellow[5] 29.977 7.986 18.500 29.255 44.962
beta3_yellow[6] 29.834 7.930 18.510 28.678 44.875
beta3_yellow[7] 30.289 8.022 18.624 29.403 44.904
beta3_yellow[8] 30.013 7.792 18.476 29.004 44.812
beta3_yellow[9] 29.649 8.001 18.372 28.546 44.741
beta3_yellow[10] 29.862 7.716 18.517 28.999 44.683
beta3_yellow[11] 45.283 0.550 43.971 45.385 45.978
beta3_yellow[12] 43.300 0.376 42.478 43.276 44.042
beta3_yellow[13] 44.875 0.404 43.995 44.953 45.560
beta3_yellow[14] 44.064 1.592 41.172 44.202 45.789
beta3_yellow[15] 45.133 0.533 44.116 45.088 45.973
beta3_yellow[16] 44.533 0.655 43.339 44.520 45.824
mu_beta0_yellow[1] 0.119 0.554 -1.071 0.139 1.210
mu_beta0_yellow[2] 0.654 0.358 -0.127 0.674 1.325
mu_beta0_yellow[3] -2.461 0.639 -3.499 -2.540 -0.900
tau_beta0_yellow[1] 1.778 2.196 0.097 1.211 6.440
tau_beta0_yellow[2] 3.242 3.950 0.306 2.214 11.698
tau_beta0_yellow[3] 1.423 2.174 0.103 0.884 5.762
beta0_black[1] 0.078 0.186 -0.297 0.085 0.428
beta0_black[2] 1.915 0.129 1.665 1.915 2.170
beta0_black[3] 1.313 0.135 1.047 1.315 1.579
beta0_black[4] 2.431 0.135 2.168 2.433 2.693
beta0_black[5] 1.672 1.895 -2.268 1.704 5.645
beta0_black[6] 1.711 1.911 -2.408 1.725 5.616
beta0_black[7] 1.571 1.960 -3.046 1.667 5.423
beta0_black[8] 1.312 0.226 0.867 1.312 1.754
beta0_black[9] 2.454 0.254 1.962 2.453 2.962
beta0_black[10] 1.479 0.138 1.206 1.479 1.752
beta0_black[11] 3.479 0.158 3.165 3.481 3.782
beta0_black[12] 4.870 0.180 4.517 4.867 5.217
beta0_black[13] 0.206 0.528 -0.564 0.037 1.126
beta0_black[14] 2.859 0.161 2.545 2.859 3.164
beta0_black[15] 1.291 0.159 0.989 1.292 1.595
beta0_black[16] 4.270 0.164 3.952 4.269 4.595
beta2_black[1] 16.125 38.601 0.002 2.143 154.072
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -0.791 3.210 -6.273 -1.098 6.768
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 36.971 7.460 19.195 40.722 44.207
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 36.157 6.312 19.707 39.042 42.684
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.279 0.197 -0.671 -0.283 0.112
beta4_black[2] 0.241 0.186 -0.129 0.240 0.613
beta4_black[3] -0.929 0.196 -1.315 -0.928 -0.552
beta4_black[4] 0.432 0.219 0.016 0.428 0.864
beta4_black[5] 0.248 2.390 -4.077 0.171 5.202
beta4_black[6] 0.297 2.373 -4.258 0.217 5.128
beta4_black[7] 0.240 2.320 -4.312 0.157 5.246
beta4_black[8] -0.713 0.374 -1.446 -0.706 0.012
beta4_black[9] 1.462 1.009 -0.194 1.368 3.700
beta4_black[10] 0.021 0.196 -0.349 0.016 0.409
beta4_black[11] -0.687 0.221 -1.122 -0.692 -0.261
beta4_black[12] 0.185 0.327 -0.424 0.178 0.837
beta4_black[13] -1.179 0.226 -1.629 -1.179 -0.739
beta4_black[14] -0.186 0.236 -0.650 -0.188 0.285
beta4_black[15] -0.881 0.224 -1.318 -0.882 -0.449
beta4_black[16] -0.590 0.233 -1.043 -0.589 -0.147
mu_beta0_black[1] 1.348 0.876 -0.629 1.378 3.069
mu_beta0_black[2] 1.626 0.882 -0.398 1.691 3.320
mu_beta0_black[3] 2.567 0.977 0.412 2.635 4.382
tau_beta0_black[1] 0.691 0.658 0.054 0.493 2.504
tau_beta0_black[2] 2.061 4.534 0.056 0.897 9.728
tau_beta0_black[3] 0.265 0.187 0.054 0.220 0.740
beta0_dsr[11] -2.876 0.291 -3.455 -2.871 -2.327
beta0_dsr[12] 4.574 0.286 4.003 4.572 5.148
beta0_dsr[13] -1.355 0.321 -1.989 -1.341 -0.764
beta0_dsr[14] -3.634 0.508 -4.638 -3.628 -2.684
beta0_dsr[15] -1.936 0.285 -2.477 -1.939 -1.359
beta0_dsr[16] -2.978 0.362 -3.687 -2.980 -2.268
beta1_dsr[11] 4.808 0.302 4.217 4.804 5.393
beta1_dsr[12] 6.609 9.528 2.218 4.982 19.078
beta1_dsr[13] 2.872 0.353 2.237 2.853 3.517
beta1_dsr[14] 6.297 0.535 5.250 6.295 7.355
beta1_dsr[15] 3.337 0.292 2.747 3.343 3.904
beta1_dsr[16] 5.793 0.384 5.054 5.794 6.537
beta2_dsr[11] -8.194 2.317 -13.444 -7.863 -4.612
beta2_dsr[12] -7.040 2.621 -12.741 -6.890 -2.303
beta2_dsr[13] -6.436 2.712 -12.485 -6.346 -1.480
beta2_dsr[14] -6.131 2.637 -11.731 -5.973 -1.825
beta2_dsr[15] -7.620 2.402 -12.996 -7.373 -3.740
beta2_dsr[16] -7.883 2.400 -13.420 -7.518 -4.120
beta3_dsr[11] 43.489 0.153 43.210 43.483 43.781
beta3_dsr[12] 33.942 0.764 32.045 34.110 34.806
beta3_dsr[13] 43.248 0.331 42.778 43.197 43.876
beta3_dsr[14] 43.355 0.245 43.075 43.280 43.996
beta3_dsr[15] 43.514 0.186 43.153 43.516 43.859
beta3_dsr[16] 43.445 0.160 43.164 43.437 43.769
beta4_dsr[11] 0.585 0.223 0.164 0.582 1.029
beta4_dsr[12] 0.247 0.440 -0.603 0.238 1.138
beta4_dsr[13] -0.169 0.221 -0.611 -0.168 0.258
beta4_dsr[14] 0.148 0.252 -0.345 0.147 0.644
beta4_dsr[15] 0.716 0.224 0.270 0.716 1.151
beta4_dsr[16] 0.154 0.232 -0.302 0.161 0.595
beta0_slope[11] -1.843 0.151 -2.135 -1.846 -1.541
beta0_slope[12] -4.480 0.259 -5.014 -4.472 -3.998
beta0_slope[13] -1.333 0.182 -1.720 -1.323 -1.013
beta0_slope[14] -2.681 0.165 -3.011 -2.682 -2.357
beta0_slope[15] -1.338 0.149 -1.631 -1.336 -1.051
beta0_slope[16] -2.729 0.160 -3.041 -2.729 -2.419
beta1_slope[11] 4.495 0.227 4.056 4.488 4.967
beta1_slope[12] 3.976 0.457 3.075 3.966 4.867
beta1_slope[13] 2.694 0.392 2.198 2.636 3.683
beta1_slope[14] 6.340 0.418 5.547 6.333 7.155
beta1_slope[15] 3.000 0.210 2.586 3.001 3.405
beta1_slope[16] 5.297 0.283 4.747 5.291 5.851
beta2_slope[11] 8.626 2.298 5.042 8.299 13.955
beta2_slope[12] 6.601 2.921 1.166 6.643 12.848
beta2_slope[13] 5.452 3.081 0.476 5.331 11.855
beta2_slope[14] 6.436 2.612 2.215 6.239 12.052
beta2_slope[15] 8.197 2.376 4.499 7.861 13.730
beta2_slope[16] 7.814 2.322 4.222 7.452 13.248
beta3_slope[11] 43.459 0.131 43.216 43.457 43.710
beta3_slope[12] 43.348 0.293 42.836 43.307 43.933
beta3_slope[13] 43.442 0.368 42.896 43.398 44.014
beta3_slope[14] 43.268 0.137 43.093 43.233 43.617
beta3_slope[15] 43.493 0.160 43.201 43.491 43.796
beta3_slope[16] 43.372 0.144 43.145 43.352 43.695
beta4_slope[11] -0.740 0.168 -1.070 -0.739 -0.408
beta4_slope[12] -1.156 0.465 -2.183 -1.121 -0.361
beta4_slope[13] 0.079 0.165 -0.246 0.079 0.398
beta4_slope[14] -0.088 0.200 -0.472 -0.092 0.307
beta4_slope[15] -0.764 0.163 -1.091 -0.763 -0.452
beta4_slope[16] -0.171 0.177 -0.518 -0.175 0.163
sigma_H[1] 0.200 0.055 0.102 0.196 0.319
sigma_H[2] 0.172 0.030 0.119 0.169 0.238
sigma_H[3] 0.196 0.042 0.120 0.194 0.286
sigma_H[4] 0.419 0.078 0.298 0.411 0.601
sigma_H[5] 0.994 0.208 0.608 0.989 1.416
sigma_H[6] 0.387 0.204 0.025 0.381 0.820
sigma_H[7] 0.314 0.067 0.211 0.306 0.470
sigma_H[8] 0.414 0.090 0.267 0.404 0.602
sigma_H[9] 0.526 0.123 0.332 0.510 0.806
sigma_H[10] 0.215 0.043 0.143 0.211 0.311
sigma_H[11] 0.278 0.046 0.200 0.273 0.381
sigma_H[12] 0.435 0.166 0.205 0.409 0.765
sigma_H[13] 0.216 0.038 0.150 0.214 0.295
sigma_H[14] 0.510 0.094 0.348 0.502 0.715
sigma_H[15] 0.247 0.041 0.181 0.244 0.336
sigma_H[16] 0.223 0.044 0.149 0.219 0.324
lambda_H[1] 3.012 3.929 0.165 1.669 13.818
lambda_H[2] 8.205 7.677 0.710 5.952 28.735
lambda_H[3] 6.144 8.454 0.257 3.247 28.617
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.764 8.255 0.036 1.048 25.740
lambda_H[6] 7.708 14.893 0.009 0.930 51.046
lambda_H[7] 0.011 0.009 0.002 0.009 0.033
lambda_H[8] 8.101 10.091 0.106 4.538 36.141
lambda_H[9] 0.015 0.010 0.003 0.013 0.039
lambda_H[10] 0.334 1.124 0.037 0.196 1.171
lambda_H[11] 0.266 0.418 0.012 0.130 1.253
lambda_H[12] 4.929 6.425 0.202 2.792 22.350
lambda_H[13] 3.538 3.225 0.252 2.627 11.621
lambda_H[14] 3.426 4.479 0.223 2.070 14.841
lambda_H[15] 0.027 0.079 0.003 0.016 0.106
lambda_H[16] 0.843 1.290 0.044 0.438 3.989
mu_lambda_H[1] 4.331 1.877 1.254 4.185 8.482
mu_lambda_H[2] 3.849 1.944 0.703 3.713 7.981
mu_lambda_H[3] 3.517 1.836 0.782 3.233 7.654
sigma_lambda_H[1] 8.623 4.242 2.147 8.005 18.178
sigma_lambda_H[2] 8.437 4.662 1.240 7.851 18.272
sigma_lambda_H[3] 6.280 3.957 1.070 5.405 15.960
beta_H[1,1] 6.895 1.039 4.504 7.050 8.526
beta_H[2,1] 9.882 0.502 8.812 9.913 10.774
beta_H[3,1] 8.001 0.782 6.028 8.103 9.229
beta_H[4,1] 9.331 7.954 -6.746 9.561 24.632
beta_H[5,1] 0.112 2.322 -4.656 0.302 4.013
beta_H[6,1] 3.160 3.940 -6.664 4.475 7.613
beta_H[7,1] -0.565 6.196 -13.679 -0.088 10.302
beta_H[8,1] 1.346 3.751 -2.433 1.206 3.509
beta_H[9,1] 12.851 5.603 1.442 12.859 24.157
beta_H[10,1] 7.080 1.724 3.515 7.148 10.408
beta_H[11,1] 5.137 3.497 -2.824 5.868 9.844
beta_H[12,1] 2.612 1.035 0.780 2.549 4.941
beta_H[13,1] 9.044 0.953 7.177 9.132 10.494
beta_H[14,1] 2.169 1.047 0.172 2.189 4.199
beta_H[15,1] -6.093 3.773 -12.751 -6.320 2.045
beta_H[16,1] 3.420 2.655 -1.068 3.073 9.547
beta_H[1,2] 7.898 0.234 7.433 7.903 8.355
beta_H[2,2] 10.021 0.139 9.742 10.025 10.287
beta_H[3,2] 8.951 0.203 8.541 8.951 9.344
beta_H[4,2] 3.554 1.491 0.779 3.489 6.604
beta_H[5,2] 1.931 0.940 0.091 1.962 3.741
beta_H[6,2] 5.735 1.059 3.210 5.903 7.380
beta_H[7,2] 2.989 1.179 0.905 2.921 5.507
beta_H[8,2] 2.980 1.093 1.382 3.118 4.232
beta_H[9,2] 3.534 1.122 1.473 3.511 5.875
beta_H[10,2] 8.210 0.353 7.472 8.230 8.875
beta_H[11,2] 9.765 0.630 8.810 9.646 11.198
beta_H[12,2] 3.938 0.373 3.231 3.927 4.685
beta_H[13,2] 9.117 0.260 8.674 9.101 9.635
beta_H[14,2] 4.019 0.354 3.349 4.015 4.731
beta_H[15,2] 11.357 0.680 9.911 11.388 12.581
beta_H[16,2] 4.536 0.816 3.005 4.532 6.151
beta_H[1,3] 8.462 0.252 8.008 8.451 8.962
beta_H[2,3] 10.066 0.120 9.826 10.067 10.307
beta_H[3,3] 9.610 0.167 9.289 9.605 9.956
beta_H[4,3] -2.521 0.916 -4.319 -2.535 -0.752
beta_H[5,3] 3.832 0.589 2.644 3.837 4.961
beta_H[6,3] 8.009 1.177 6.386 7.643 10.526
beta_H[7,3] -3.115 0.690 -4.474 -3.112 -1.804
beta_H[8,3] 5.246 0.503 4.647 5.178 6.210
beta_H[9,3] -2.857 0.735 -4.330 -2.861 -1.391
beta_H[10,3] 8.681 0.282 8.152 8.670 9.242
beta_H[11,3] 8.543 0.282 7.935 8.570 9.033
beta_H[12,3] 5.256 0.324 4.499 5.298 5.765
beta_H[13,3] 8.842 0.177 8.492 8.846 9.182
beta_H[14,3] 5.713 0.279 5.095 5.735 6.214
beta_H[15,3] 10.365 0.315 9.761 10.366 10.988
beta_H[16,3] 6.249 0.598 4.959 6.302 7.282
beta_H[1,4] 8.253 0.172 7.894 8.262 8.553
beta_H[2,4] 10.127 0.120 9.864 10.135 10.343
beta_H[3,4] 10.117 0.161 9.763 10.124 10.398
beta_H[4,4] 11.809 0.451 10.888 11.816 12.670
beta_H[5,4] 5.472 0.744 4.286 5.392 7.159
beta_H[6,4] 7.064 0.928 4.955 7.340 8.333
beta_H[7,4] 8.323 0.367 7.601 8.329 9.004
beta_H[8,4] 6.710 0.262 6.233 6.724 7.144
beta_H[9,4] 7.216 0.476 6.289 7.215 8.141
beta_H[10,4] 7.758 0.241 7.309 7.750 8.254
beta_H[11,4] 9.379 0.198 8.982 9.373 9.762
beta_H[12,4] 7.143 0.212 6.751 7.132 7.595
beta_H[13,4] 9.045 0.142 8.759 9.051 9.331
beta_H[14,4] 7.729 0.215 7.319 7.725 8.167
beta_H[15,4] 9.468 0.235 8.995 9.459 9.952
beta_H[16,4] 9.348 0.237 8.920 9.335 9.840
beta_H[1,5] 8.980 0.142 8.704 8.987 9.257
beta_H[2,5] 10.780 0.095 10.595 10.780 10.970
beta_H[3,5] 10.917 0.173 10.612 10.909 11.285
beta_H[4,5] 8.367 0.466 7.495 8.350 9.314
beta_H[5,5] 5.424 0.580 4.093 5.470 6.440
beta_H[6,5] 8.811 0.635 7.888 8.667 10.322
beta_H[7,5] 6.753 0.357 6.053 6.746 7.489
beta_H[8,5] 8.214 0.226 7.848 8.195 8.631
beta_H[9,5] 8.197 0.480 7.244 8.186 9.157
beta_H[10,5] 10.088 0.229 9.629 10.093 10.541
beta_H[11,5] 11.513 0.224 11.066 11.512 11.946
beta_H[12,5] 8.489 0.204 8.094 8.486 8.903
beta_H[13,5] 10.006 0.130 9.749 10.008 10.255
beta_H[14,5] 9.194 0.231 8.780 9.181 9.683
beta_H[15,5] 11.165 0.245 10.671 11.167 11.634
beta_H[16,5] 9.919 0.175 9.556 9.923 10.252
beta_H[1,6] 10.192 0.182 9.869 10.180 10.576
beta_H[2,6] 11.514 0.109 11.302 11.515 11.723
beta_H[3,6] 10.811 0.161 10.472 10.822 11.092
beta_H[4,6] 12.904 0.810 11.236 12.934 14.449
beta_H[5,6] 5.876 0.613 4.699 5.868 7.137
beta_H[6,6] 8.779 0.659 7.100 8.900 9.714
beta_H[7,6] 9.893 0.589 8.722 9.913 11.041
beta_H[8,6] 9.506 0.285 9.031 9.530 9.951
beta_H[9,6] 8.491 0.785 6.954 8.477 10.032
beta_H[10,6] 9.508 0.317 8.852 9.523 10.057
beta_H[11,6] 10.808 0.352 10.071 10.842 11.425
beta_H[12,6] 9.368 0.257 8.884 9.355 9.910
beta_H[13,6] 11.047 0.169 10.744 11.036 11.389
beta_H[14,6] 9.823 0.296 9.209 9.835 10.389
beta_H[15,6] 10.841 0.421 10.032 10.835 11.689
beta_H[16,6] 10.534 0.235 10.032 10.550 10.960
beta_H[1,7] 10.888 0.831 8.888 10.983 12.247
beta_H[2,7] 12.222 0.434 11.338 12.221 13.091
beta_H[3,7] 10.541 0.675 9.045 10.612 11.644
beta_H[4,7] 2.412 4.114 -5.358 2.250 11.009
beta_H[5,7] 6.403 1.772 3.252 6.317 10.257
beta_H[6,7] 9.580 2.387 4.731 9.522 15.672
beta_H[7,7] 10.498 2.955 4.681 10.502 16.410
beta_H[8,7] 10.928 1.051 9.313 10.878 12.566
beta_H[9,7] 4.316 3.945 -3.435 4.295 11.890
beta_H[10,7] 9.879 1.466 7.081 9.790 13.068
beta_H[11,7] 10.996 1.757 7.819 10.847 14.712
beta_H[12,7] 10.008 0.933 7.983 10.088 11.578
beta_H[13,7] 11.676 0.770 9.824 11.784 12.849
beta_H[14,7] 10.437 0.962 8.422 10.468 12.141
beta_H[15,7] 12.023 2.204 7.755 12.004 16.401
beta_H[16,7] 12.303 1.218 10.268 12.130 15.028
beta0_H[1] 9.291 12.960 -16.861 9.147 37.386
beta0_H[2] 10.669 6.462 -2.656 10.745 23.318
beta0_H[3] 9.929 10.182 -10.612 9.950 31.043
beta0_H[4] 6.044 181.823 -366.590 1.905 385.897
beta0_H[5] 3.647 22.857 -46.350 4.450 46.459
beta0_H[6] 7.086 50.681 -101.974 7.637 114.732
beta0_H[7] 3.064 145.661 -298.328 3.822 292.662
beta0_H[8] 6.996 32.971 -15.300 6.340 26.331
beta0_H[9] 5.377 118.568 -235.229 7.954 249.100
beta0_H[10] 9.094 31.925 -54.230 8.665 77.407
beta0_H[11] 10.428 49.637 -93.778 9.682 112.763
beta0_H[12] 6.683 11.168 -15.315 6.506 29.573
beta0_H[13] 9.871 11.994 -11.586 9.910 30.800
beta0_H[14] 7.328 11.182 -14.674 7.072 31.329
beta0_H[15] 6.476 107.437 -212.009 8.425 224.133
beta0_H[16] 7.996 24.784 -47.096 8.798 57.873